MN Mathematics Standards
2007 Revision
Grades 3-6
I.
Number & Operation
Grade 3 Standard 1.1: Compare
Grade 4 Standard 1.1:
Grade 5 Standard 1.1: Divide
Grade 6 Standard 1.1: Read,
and represent whole numbers up to
100,000 with an emphasis on place
value and equity.
Demonstrate mastery of multiplication
and division basic facts; multiply multidigit numbers; solve real-world and
mathematical problems using
arithmetic.
multi-digit numbers; solve real-world
and mathematical problems using
arithmetic.
write, represent and compare
positive rational numbers expressed
as fractions, decimals, percents and
ratios; write positive integers as
products of factors; use these
representations in real-world and
mathematical situations.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.1.1.1 Read, write and represent whole
numbers up to 100,000. Representations
may include numerals, expressions with
operations, words, pictures, number lines,
and manipulative such as bundles of
sticks and base 10 blocks.
4.1.1.1 Demonstrate fluency with
multiplication and division facts.
6.1.1.1 Locate positive rational
numbers on a number line and plot
pairs of positive rational numbers on
a coordinate grid.
3.1.1.2 Use place value to describe
whole numbers between 1000 and
100,000 in terms of ten thousands,
thousands, hundreds, tens and ones.
4.1.1.3 Multiply multi-digit numbers,
using efficient and generalizable
procedures, based on knowledge of
place value, including standard
algorithms.
5.1.1.1 Divide multi-digit numbers,
using efficient and generalizable
procedures, based on knowledge of
place value, including standard
algorithms. Recognize that quotients
can be represented in a variety of
ways, including a whole number with
a remainder, a fraction or mixed
number, or a decimal.
Example: Writing 54,873 is a shorter
way of writing the following sums:
5 ten thousands + 4 thousands + 8 hundreds
+ 7 tens + 3 ones
54 thousands + 8 hundreds + 7 tens + 3
ones.
3.1.1.3 Find 10,000 more or 10,000 less
than a given five-digit number. Find 1000
more or 1000 less than a given four- or
five-digit number. Find 100 more or 100
less than a given four- or five-digit
number.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
4.1.1.2 Use an understanding of place
value to multiply a number by 10, 100
and 1000.
4.1.1.4 Estimate products and
quotients of multi-digit whole numbers
by using rounding, benchmarks and
place value to assess the
reasonableness of results.
Example: 53 × 38 is between 50 × 30
and 60 × 40, or between 1500 and 2400,
and 411/73 is between 5 and 6..
4.1.1.5 Solve multi-step real-world and
mathematical problems requiring the
use of addition, subtraction and
multiplication of multi-digit whole
numbers. Use various strategies,
including the relationship between
operations, the use of technology, and
the context of the problem to assess
the reasonableness of results.
Example: Dividing 153 by 7 can be
used to convert the improper fraction
153 to the mixed number 21 6 .
7
7
5.1.1.2 Consider the context in
which a problem is situated to select
the most useful form of the quotient
for the solution and use the context
to interpret the quotient
appropriately.
Example: If 77 amusement ride tickets
are to be distributed equally among 4
children, each child will receive 19
tickets, and there will be one left over.
If $77 is to be distributed equally
among 4 children, each will receive
$19.25, with nothing left over.
5.1.1.3 Estimate solutions to
arithmetic problems in order to
assess the reasonableness of
results.
6.1.1.2 Compare positive rational
numbers represented in various
forms. Use the symbols < and >.
Example:
1
2
> 0.36.
6.1.1.3 Understand that percent
represents parts out of 100 and
ratios to 100.
Example: 75% is equivalent to the
ratio 75 to 100, which is equivalent to
the ratio 3 to 4.
6.1.1.4 Determine equivalences
among fractions, decimals and
percents; select among these
representations to solve problems.
Example: If a woman making $25 an
hour gets a 10% raise, she will make
an additional $2.50 an hour, because
$2.50 is 1 or 10% of $25.
10
6.1.1.5 Factor whole numbers;
express a whole number as a
product of prime factors with
exponents.
Example: 24 = 23 x 3
2
I.
Number & Operation (continued)
Grade 3 Standard 1.1 (cont):
Grade 4 Standard 1.1 (cont):
Grade 5 Standard 1.1 (cont.):
Grade 6 Standard 1.1 (cont.):
Compare and represent whole numbers
up to 100,000 with an emphasis on
place value and equity.
Demonstrate mastery of multiplication
and division basic facts; multiply multidigit numbers; solve real-world and
mathematical problems using
arithmetic.
Divide multi-digit numbers; solve
real-world and mathematical
problems using arithmetic.
Read, write, represent and compare
positive rational numbers expressed
as fractions, decimals, percents and
ratios; write positive integers as
products of factors; use these
representations in real-world and
mathematical situations.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.1.1.4 Round numbers to the nearest
10,000, 1000, 100, and 10. Round up and
round down to estimate sums and
differences.
4.1.1.6 Use strategies and algorithms
based on knowledge of place value,
equality and properties of operations to
divide multi-digit whole numbers by
one- or two-digit numbers. Strategies
may include mental strategies, partial
quotients, the commutative,
associative, and distributive properties
and repeated subtraction.
5.1.1.4 Solve real-world and
mathematical problems requiring
addition, subtraction, multiplication
and division of multi-digit whole
numbers. Use various strategies,
including the inverse relationships
between operations, the use of
technology, and the context of the
problem to assess the
reasonableness of results.
6.1.1.6 Determine greatest common
factors and least common multiples.
Use common factors and common
multiples to calculate with fractions
and find equivalent fractions.
Example: 8726 rounded to the
nearest 1000 is 9000, rounded to the
nearest 100 is 8700, and rounded to
the nearest 10 is 8730.
Example 473– 291 is between 400 –
300 and 500 – 200, or between 100
and 300.
3.1.1.5 Compare and order whole
numbers up to 100,000.
Example: A group of 324 students is
going to a museum in 6 buses. If each
bus has the same number of students,
how many students will be on each bus?
Example: The calculation 117 ÷ 9 = 13
can be checked by multiplying 9 and
13.
Example: Factor the numerator
and denominator of a fraction to
determine an equivalent fraction.
6.1.1.7 Convert between equivalent
representations of positive rational
numbers.
Example: Express
7 3  7  3  1 3
7
7 7
7
MN Mathematics Standards - 2007 revision
Grades 3 - 6
10
7
as
.
3
I.
Number & Operation (continued)
Grade 3 Standard 1.2: Add and
Grade 4 Standard 1.2: Represent
Grade 5 Standard 1.2: Read,
Grade 6 Standard 1.2:
subtract multi-digit whole numbers;
represent multiplication and division in
various ways; solve real-world and
mathematical problems using arithmetic.
and compare fractions and decimals in
real-world and mathematical situations;
use place value to understand how
decimals represent quantities.
write, represent and compare
fractions and decimals; recognize
and write equivalent fractions;
convert between fractions and
decimals; use fractions and decimals
in real-world and mathematical
situations.
Understand the concept of ratio and
its relationship to fractions and to the
multiplication and division of whole
numbers. Use ratios to solve realworld and mathematical problems.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.1.2.1 Add and subtract multi-digit
numbers, using efficient and
generalizable procedures based on
knowledge of place value, including
standard algorithms.
4.1.2.1 Represent equivalent fractions
using fraction models such as parts of
a set, fraction circles, fraction strips,
number lines and other manipulatives.
Use the models to determine
equivalent fractions.
5.1.2.1 Read and write decimals
using place value to describe
decimals in terms of groups from
millionths to millions.
6.1.2.1: Identify and use ratios to
compare quantities; understand that
comparing quantities using ratios is
not the same as comparing
quantities using subtraction.
3.1.2.2 Use addition and subtraction to
solve real-world and mathematical
problems involving whole numbers.
Use various strategies, including the
relationship between addition and
subtraction, the use of technology, and
the context of the problem to assess the
reasonableness of results.
Example: The calculation 117–83=34
can be checked by adding 83 and 34.
3.1.2.3 Represent multiplication facts
by using a variety of approaches, such
as repeated addition, equal-sized
groups, arrays, area models, equal
jumps on a number line and skip
counting. Represent division facts by
using a variety of approaches, such as
repeated subtraction, equal sharing and
forming equal groups. Recognize the
relationship between multiplication and
division.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
4.1.2.2 Locate fractions on a number
line. Use models to order and compare
whole numbers and fractions, including
mixed numbers and improper fractions.
Example: Locate
5
3
and 1
3
4
on a number
line and give a comparison statement
about these two fractions, such as " 5 is
3
less than 1 34 ."
4.1.2.3 Use fraction models to add
and subtract fractions with like
denominators in real-world and
mathematical situations. Develop a
rule for addition and subtraction of
fractions with like denominators.
Example: Possible names for the
number 0.0037 are: 37 ten thousandths
3 thousandths + 7 ten thousandths;
a possible name for the number 1.5 is
15 tenths.
5.1.2.2 Find 0.1 more than a
number and 0.1 less than a number.
Find 0.01 more than a number and
0.01 less than a number. Find 0.001
more than a number and 0.001 less
than a number.
5.1.2.3 Order fractions and
decimals, including mixed numbers
and improper fractions, and locate
on a number line.
Example: Which is larger 1.25 or
6
5
?
Example: In order to work properly, a
part must fit through a 0.24 inch wide
space. If a part is 14 inch wide, will it
fit?
Example: In a classroom with 15 boys
and 10 girls, compare the numbers by
subtracting (there are 5 more boys
than girls) or by dividing (there are 2.5
times as many boys as girls). The
comparison using division may be
expressed as a ratio of boys to girls (3
to 2 or 3:2 or 1.5 to 1).
6.1.2.2 Apply the relationship
between ratios, equivalent fractions
and percents to solve problems in
various contexts, including those
involving mixtures and
concentrations.
Example: If 5 cups of trail mix contains
2 cups of raisins, the ratio of raisins to
trail mix is 2 to 5. This ratio
corresponds to the fact that the raisins
are 2 of the total, or 40% of the total.
5
And if one trail mix consists of 2 parts
peanuts to 3 parts raisins, and another
consists of 4 parts peanuts to 8 parts
raisins, then the first mixture has a
higher concentration of peanuts.
4
I.
Number & Operation (continued)
Grade 3 Standard 1.2 (cont.): Add
Grade 4 Standard 1.2 (cont.):
Grade 5 Standard 1.2 (cont.):
Grade 6 Standard 1.2 (cont.):
and subtract multi-digit whole numbers;
represent multiplication and division in
various ways; solve real-world and
mathematical problems using arithmetic.
Represent and compare fractions and
decimals in real-world and
mathematical situations; use place
value to understand how decimals
represent quantities.
Read, write, represent and compare
fractions and decimals; recognize
and write equivalent fractions;
convert between fractions and
decimals; use fractions and decimals
in real-world and mathematical
situations.
Understand the concept of ratio and
its relationship to fractions and to the
multiplication and division of whole
numbers. Use ratios to solve realworld and mathematical problems.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.1.2.4 Solve real-world and
mathematical problems involving
multiplication and division, including
both “how many in each group” and
“how many groups” division problems.
4.1.2.4 Read and write decimals with
words and symbols; use place value to
describe decimals in terms of
thousands, hundreds, tens, ones,
tenths, hundredths and thousandths.
5.1.2.4 Recognize and generate
equivalent decimals. Fractions,
mixed numbers and improper
fractions in various contexts.
6.1.2.3 Determine the rate for ratios
of quantities with different units.
Example: You have 27 people and 9
tables. If each table seats the same
number of people, how many people
will you put at each table?
Example: If you have 27 people and
tables that will hold 9 people, how
many tables will you need?
3.1.2.5 Use strategies and algorithms
based on knowledge of place value,
equality and properties of addition and
multiplication to multiply a two- or threedigit number by a one-digit number.
Strategies may include mental
strategies, partial products, the standard
algorithm, and the commutative,
associative, and distributive properties.
Example: 9 × 26 = 9 × (20 + 6) = 9 ×
20 + 9 × 6 = 180 + 54 = 234.
Example: Writing 362.45 is a shorter way
of writing the sum: 3 hundreds + 6 tens +
2 ones + 4 tenths + 5 hundredths,
which can also be written as: three
hundred sixty-two and forty-five
hundredths.
4.1.2.5 Compare and order decimals
and whole numbers using place value,
a number line and models such as
grids and base 10 blocks.
4.1.2.6 Read and write tenths and
hundredths in decimal and fraction
notations using words and symbols;
know the fraction and decimal
equivalents for halves and fourths.
Example:
1
2
= 0.5 = 0.50 and
7
4
Example: When comparing 1.5 and 19
12 ,
note that 1.5 =
1.5 <
19
12
11
2
=
16
12
=
18
12
, so
.
5.1.2.5 Round numbers to the
nearest 0.1, 0.01and 0.001.
Example: Fifth grade students used a
calculator to find the mean of the
monthly allowance in their class. The
calculator display shows 25.80645161.
Round this number to the nearest cent.
Example: 60 miles for every 3
hours is equivalent to 20 miles for
every one hour (20 mph).
6.1.2.4 Use reasoning about
multiplication and division to solve
ratio and rate problems.
Example: If 5 items cost $3.75,
and all items are the same price,
then 1 item costs 75 cents, so 12
items cost $ 9.00.
= 1 34 =
1.75, which can also be written as one
and three-fourths or one and seventy-five
hundredths.
4.1.2.7 Round decimals to the nearest
tenth.
Example: The number 0.36 rounded to
the nearest tenth is 0.4.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
5
I.
Number & Operation (continued)
Grade 3 Standard 1.3: Understand
Grade 5 Standard 1.3: Add and
Grade 6 Standard 1.3: Multiply
meanings and uses of fractions in realworld and mathematical situations.
subtract fractions, mixed numbers
and decimals to solve real-world and
mathematical problems.
and divide decimals, fractions and
mixed numbers; solve real-world and
mathematical problems using
arithmetic with positive rational
numbers.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
5.1.3.1 Add and subtract decimals
and fractions, using efficient and
generalizable procedures, including
standard algorithms.
6.1.3.1 Multiply and divide decimals
and fractions, using efficient and
generalizable procedures, including
standard algorithms.
6.1.3.2 Use the meanings of fractions,
multiplication, division, and the inverse
relationship between multiplication and
division to make sense of procedures
for multiplying and dividing fractions.
3.1.3.1 Read and write fractions with
words and symbols. Recognize that
fractions can be used to represent parts
of a whole, parts of a set, points on a
number line, or distances on a number
line.
Example: Parts of a shape (3/4 of a
pie), parts of a set (3 out of 4 people),
and measurements (3/4 of an inch).
3.1.3.2 Understand that the size of a
fractional part is relative to the size of
the whole.
Example: One-half of a small pizza is
smaller than one-half of a large pizza,
but both represent one-half.
3.1.3.3 Order and compare units of
fractions and fractions with like
denominators by using models and an
understanding of the concept of
numerator and denominator.
Grade 4 Standard
There are no further standards in
this category for 4th grade.
5.1.3.2 Model addition and
subtraction of fractions and decimals
using a variety of representations.
Example: Represent
2
1

3
4
2
1

3
4
and
into 4 columns and 3 rows and shading
the appropriate parts or by using
fraction circles or bars.
5.1.3.3 Estimate sums and
differences of decimals and fractions
to assess the reasonableness of
results.
Example: Recognize that 12 52  3 34 is
between 8 and 9 (since
2
5

3
4
).
5.1.3.4 Solve real-world and
mathematical problems requiring
addition and subtraction of decimals,
fractions and mixed numbers,
including those involving
measurement geometry and data.
Example: Calculate the perimeter of
the soccer field when the length is
109.7 meters and the width is 73.1
meters.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
12  3 means
4
2  4  5 means 5  4  2
6 5 3
3 5 6
Example: Just as
by drawing a rectangle divided
12  3  4
,
.
6.1.3.3 Calculate the percent of a
number and determine what percent
one number is of another number to
solve problems in various contexts.
Example: If John has $45 and
spends $15, what percent of his
money did he keep?
6.1.3.4 Solve real-world and
mathematical problems requiring
arithmetic with decimals, fractions, and
mixed numbers.
6.1.3.5 Estimate solutions to
problems with whole numbers,
fractions and decimals and use the
estimates to assess the reasonableness of results in the context of the
problem.
Example: The sum 1  0.25 can be
3
estimated to be between ½ and 1, and
this estimate can be used to check the
result of a more detailed calculation.
6
II.
Algebra
Grade 3 Standard 2.1: Use single-
Grade 4 Standard 2.1: Use input-
Grade 5 Standard 2.1: Recognize
Grade 6 Standard 2.1: Recognize
operation input-output rules to represent
patterns and relationships and to solve
real-world and mathematical problems.
output rules, tables and charts to
represent patterns and relationships
and to solve real-world and
mathematical problems.
and represent patterns of change;
use patterns, tables, graphs and
rules to solve real-world and
mathematical problems.
and represent relationships between
varying quantities; translate from one
representation to another; use
patterns, tables, graphs and rules to
solve real-world and mathematical
problems.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.2.1.1 Create, describe, and apply
single-operation input-output rules
involving addition, subtraction and
multiplication to solve problems in
various contexts.
4.2.1.1 Create and use input-output
rules involving addition, subtraction,
multiplication and division to solve
problems in various contexts. Record
the inputs and outputs in a chart or
table.
5.2.1.1 Create and use rules, tables,
spreadsheets and graphs to describe
patterns of change and solve
problems.
6.2.1.1 Understand that a variable
can be used to represent a quantity
that can change, often in relationship
to another changing quantity. Use
variables in various contexts.
Example: Describe the relationship
between number of chairs and number
of legs by the rule that the number of
legs is four times the number of chairs.
Example: If the rule is "multiply by 3 and
add 4," record the outputs for given
inputs in a table.
Example: A student is given these three
arrangements of dots:
Identify a pattern that is consistent with
these figures, create an input-output rule
that describes the pattern, and use the
rule to find the number of dots in the 10th
figure.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
Example: An end-of-the-year party for
5th grade costs $100 to rent the room
and $4.50 for each student. Know how
to use a spreadsheet to create an
input-output table that records the total
cost of the party for any number of
students between 90 and 150.
5.2.1.2 Use a rule or table to
represent ordered pairs of positive
integers and graph these ordered
pairs on a coordinate system.
Example: If a student earns $7 an
hour in a job, the amount of money
earned can be represented by a
variable and is related to the number of
hours worked, which also can be
represented by a variable.
6.2.1.2 Represent the relationship
between two varying quantities with
function rules, graphs and tables;
translate between any two of these
representations.
Example: Describe the terms in
the sequence of perfect squares
t = 1, 4, 9, 16, . . . by using the rule
t = n2 for n = 1, 2, 3, 4, ….
7
II.
Algebra (continued)
Grade 3 Standard 2.2: Use number
Grade 4 Standard 2.2: Use number Grade 5 Standard 2.2: Use
Grade 6 Standard 2.2: Use
sentences involving multiplication and
division basic facts and unknowns to
represent and solve real-world and
mathematical problems; create realworld situations corresponding to
number sentences.
sentences involving multiplication,
division and unknowns to represent
and solve real-world and mathematical
problems; create real-world situations
corresponding to number sentences.
properties of arithmetic to generate
equivalent numerical expressions
and evaluate expressions involving
whole numbers.
properties of arithmetic to generate
equivalent numerical expressions and
evaluate expressions involving positive
rational numbers.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.2.2.1 Understand how to interpret
number sentences involving
multiplication and division basic facts
and unknowns. Create real-world
situations to represent number
sentences.
4.2.2.1 Understand how to interpret
number sentences involving
multiplication, division and unknowns.
Use real-world situations involving
multiplication or division to represent
number sentences.
5.2.2.1 Apply the commutative,
associative and distributive
properties and order of operations to
generate equivalent numerical
expressions and to solve problems
involving whole numbers.
6.2.2.1 Apply the associative,
commutative and distributive properties
and order of operations to generate
equivalent expressions and to solve
problems involving positive rational
numbers.
Example: The number sentence a × b =
60 can be represented by the situation in
which chairs are being arranged in equal
rows and the total number of chairs is
60.
Example: Purchase 5 pencils at 19
cents and 7 erasers at 19 cents. The
numerical expression is 5 × 19 + 7 ×
19 which is the same as (5 + 7) × 19.
Example: The number sentence
8 × m = 24 could be represented by the
question "How much did each ticket to
a play cost if 8 tickets totaled $24?"
3.2.2.2 Use multiplication and division
basic facts to represent a given
problem situation using a number
sentence. Use number sense and
multiplication and division basic facts to
find values for the unknowns that make
the number sentences true.
Example: Find values of the unknowns
that make each number sentence true
6=p÷9
24 = a × b
5×8=4×t
Example: How many math teams are
competing if there is a total of 45
students with 5 students on each
team? This situation can be
represented by 5 × n = 45 or 45 = n or
5
45
n
= 5.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
4.2.2.2 Use multiplication, division
and unknowns to represent a given
problem situation using a number
sentence. Use number sense,
properties of multiplication, and the
relationship between multiplication
and division to find values for the
unknowns that make the number
sentences true.
Example:
32  5  325  2165  16  2  5  16
15 6 156 353 2 9 2 5 9
Example: Use the distributive law to
write:


1  1 9  15  1  1  9  1  15  1  3  5  2  5  1 3
2 3 2 8
2 3 2 3 8 2 2 8
8
8
Example: If $84 is to be shared equally
among a group of children, the amount
of
money each child receives can be
determined using the number sentence
84 ÷ n = d.
Example: Find values of the unknowns
that make each number sentence true:
12 × m = 36
s = 256 ÷ t
8
II.
Algebra (continued)
Grade 3 Standards
There are no further standards in
this category for 3rd grade.
Grade 4 Standards
There are no further standards in
this category for 2nd grade.
Grade 5 Standard 2.2: Use
Grade 6 Standard 2.2: Use
properties of arithmetic to generate
equivalent numerical expressions
and evaluate expressions involving
whole numbers.
properties of arithmetic to generate
equivalent numerical expressions and
evaluate expressions involving positive
rational numbers.
Benchmarks The student will:
Benchmarks The student will:
5.2.2.1 Apply the commutative,
associative and distributive
properties and order of operations to
generate equivalent numerical
expressions and to solve problems
involving whole numbers.
6.2.2.1 Apply the associative,
commutative and distributive properties
and order of operations to generate
equivalent expressions and to solve
problems involving positive rational
numbers.
Example: Purchase 5 pencils at 19
cents and 7 erasers at 19 cents. The
numerical expression is 5 × 19 + 7 ×
19 which is the same as (5 + 7) × 19.
Example:
32  5  325  2165  16  2  5  16
15 6 156 353 2 9 2 5 9
Example: Use the distributive law to
write:


1  1 9  15  1  1  9  1  15  1  3  5  2  5  1 3
2 3 2 8
2 3 2 3 8 2 2 8
8
8
MN Mathematics Standards - 2007 revision
Grades 3 - 6
9
II.
Algebra (continued)
Grade 3 Standards
There are no further standards in
this category for 3rd grade.
Grade 4 Standard
There are no further standards in
this category for 2nd grade.
Grade 5 Standard 2.3: Understand
Grade 6 Standard 2.3: Understand
G
and interpret equations and inequalities
involving variables and whole numbers,
and use them to represent and solve
real-world and mathematical problems.
and interpret equations and inequalities
involving variables and positive rational
numbers. Use equations and
inequalities to represent real-world and
mathematical problems; use the idea of
maintaining equality to solve equations.
Interpret solutions in the original
context.
c
a
le
Benchmarks The student will:
Benchmarks The student will:
5.2.3.1 Determine whether an equation
or inequality involving a variable is true
or false for a given value of the variable.
6.2.3.1 Represent real-world or
mathematical situations using equations
and inequalities involving variables and
positive rational numbers.
Example: Determine whether the
inequality 1.5 + x < 10 is true for
x = 2.8, x = 8.1, or x = 9.2.same as
(5 + 7) × 19.
5.2.3.2 Represent real-world situations
using equations and inequalities
involving variables. Create real-world
situations corresponding to equations
and inequalities.
Example: 250 – 27 × a = b can be used
to represent the number of sheets of paper
remaining from a packet of 250 sheets
when each student in a class of 27 is given
a certain number of sheets.
5.2.3.3 Evaluate expressions and solve
equations involving variables when
values for the variables are given.
Example: The number of miles m in
a k kilometer race is represented by
the equation m = 0.62 k.
6.2.3.2 Solve equations involving
positive rational numbers using number
sense, properties of arithmetic and the
idea of maintaining equality on both
sides of the equation. Interpret a
solution in the original context and
assess the reasonableness of results.
Example: A cellular phone company
charges $0.12 per minute. If the bill
was $11.40 in April, how many minutes
were used?
Example: Using the formula, A= ℓw,
determine the area when the length is 5,
and the width 6, and find the length when
the area is 24 and the width is 4.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
10
III.
Geometry & Measurement
Grade 3 Standard 3.1: Use
Grade 4 Standard 3.1: Name,
Grade 5 Standard 3.1: Describe,
Grade 6 Standard 3.1: Calculate
geometric attributes to describe and
create shapes in various contexts.
describe, classify and sketch polygons.
classify, and draw representations of
three-dimensional figures.
perimeter, area, surface area and
volume of two- and threedimensional figures to solve realworld mathematical problems.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.3.1.1 Identify parallel and
perpendicular lines in various contexts,
and use them to describe and create
geometric shapes, such as right
triangles, rectangles, parallelograms
and trapezoids.
4.3.1.1 Describe, classify and sketch
triangles, including equilateral, right,
obtuse and acute triangles. Recognize
triangles in various contexts.
5.3.1.1 Describe and classify threedimensional figures including cubes,
prisms and pyramids by the number
of edges, faces or vertices as well as
the types of faces.
6.3.1.1 Calculate the surface area
and volume of prisms and use
appropriate units, such as cm2 and
cm3. Justify the formulas used.
Justifications may involve
decomposition, nets or other models.
3.3.1.2 Sketch polygons with a given
number of sides or vertices (corners),
such as pentagons, hexagons and
octagons.
4.3.1.2 Describe, classify and draw
quadrilaterals, including squares,
rectangles, trapezoids, rhombuses,
parallelograms and kites. Recognize
quadrilaterals in various contexts.
5.3.1.2 Recognize and draw a net
for a three-dimensional figure.
Example: 50 cents can be made up of
2 quarters, or 4 dimes and 2 nickels, or
many other combinations.
Example: The surface area of a
triangle prism can be found by
decomposing the surface into two
triangles and three rectangles.
6.3.1.2 Calculate the area of
quadrilaterals. Quadrilaterals
include squares, rectangles,
rhombuses, parallelograms,
trapezoids and kites. When formulas
are used, be able to explain why
they are valid.
Example: The area of a kite is one-half
the product of the lengths of the
diagonals, and this can be justified by
decomposing the kite into two triangles.
6.3.1.3 Estimate the perimeter and
area of irregular figures on a grid
when they cannot be decomposed
into common figures and use correct
units, such as cm and cm2.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
11
III.
Geometry & Measurement (continued)
Grade 3 Standard 3.2: Understand
Grade 4 Standard 3.2: Understand
Grade 5 Standard 3.2: Determine
Grade 6 Standard 3.2:
perimeter as a measurable attribute of
real-world and mathematical objects.
Use various tools to measure distances.
angle and area as measurable
attributes of real-world and
mathematical objects. Use various
tools to measure angles and areas.
the area of triangles and
quadrilaterals; determine the surface
area and volume of rectangular
prisms in various contexts.
Understand and use relationships
between angles in geometric figures.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.3.2.1 Use half units when measuring
distances.
4.3.2.1 Measure angles in geometric
figures and real-world objects with a
protractor or angle ruler.
5.3.2.1 Develop and use formulas to
determine the area of triangles,
parallelograms and figures that can
be decomposed into triangles.
6.3.2.1 Solve problems using the
relationships between the angles
formed by intersecting lines.
Example: Measure a person's height
to the nearest half inch.
3.3.2.2 Find the perimeter of a polygon
by adding the lengths of the sides.
3.3.2.3 Measure distances around
objects.
Example: Measure the distance
around a classroom, or measure a
person's wrist size.
4.3.2.2 Compare angles according to
size. Classify angles as acute, right
and obtuse.
Example: Compare different hockey
sticks according to the angle between the
blade and the shaft.
4.3.2.3 Understand that the area of a
two-dimensional figure can be found
by counting the total number of same
size square units that cover a shape
without gaps or overlaps. Justify why
length and width are multiplied to find
the area of a rectangle by breaking the
rectangle into one unit by one unit
squares and viewing these as grouped
into rows and columns.
Example: How many copies of a square
sheet of paper are needed to cover the
classroom door? Measure the length and
width of the door to the nearest inch and
compute the area of the door.
4.3.2.4 Find the areas of geometric
figures and real-world objects that can
be divided into rectangular shapes.
Use square units to label area
measurements.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
5.3.2.2 Use various tools and
strategies to measure the volume
and surface area of objects that are
shaped like rectangular prisms.
Example: Use a net or decompose
the surface into rectangles.
Example: Measure the volume of a
cereal box by using a ruler to measure
its height, width and length, or by filling
it with cereal and then emptying the
cereal into containers of known
volume.
5.3.2.3 Understand that the volume
of a three-dimensional figure can be
found by counting the total number
of same-sized cubic units that fill a
shape without gaps or overlaps. Use
cubic units to label volume
measurements.
Example: Use cubes to find the
volume of a small box.
5.3.2.4 Develop and use the
formulas V = ℓwh and V = Bh to
determine the volume of rectangular
prisms. Justify why base area B and
height h are multiplied to find the
volume of a rectangular prism by
breaking the prism into layers of unit
cubes.
Example: If two streets cross,
forming four corners such that one
of the corners forms an angle of
120˚, determine the measures of
the remaining three angles.
Example: Recognize that pairs of
interior and exterior angles in polygons
have measures that sum to 180˚.
6.3.2.2 Determine missing angle
measures in a triangle using the fact
that the sum of the interior angles of
a triangle is 180˚. Use models of
triangles to illustrate this fact.
Example: Cut a triangle out of paper,
tear off the corners and rearrange
these corners to form a straight line.
Example: Recognize that the
measures of the two acute angles in a
right triangle sum to 90˚.
6.3.2.3 Develop and use formulas
for the sums of the interior angles of
polygons by decomposing them into
triangles.
12
III.
Geometry & Measurement (continued)
Grade 3 Standard 3.3: Use time,
Grade 4 Standard 3.3: Use
money and temperature to solve realworld and mathematical problems.
translations, reflections and rotations
to establish congruency and
understand symmetries.
Benchmarks The student will:
Benchmarks The student will:
3.3.3.1 Tell time to the minute, using
digital and analog clocks. Determine
elapsed time to the minute.
Example: Your trip began at 9:50 a.m.
and ended at 3:10 p.m. How long were
you traveling?
3.3.3.2 Know relationships among units
of time.
Example: Know the number of minutes
in an hour, days in a week and months
in a year.
3.3.3.3 Make change up to one dollar in
several different ways, including with as
few coins as possible.
4.3.3.1 Apply translations (slides) to
figures.
4.3.3.2 Apply reflections (flips) to
figures by reflecting over vertical or
horizontal lines and relate reflections to
lines of symmetry.
4.3.3.3 Apply rotations (turns) of 90
clockwise or counter clockwise.
4.3.3.4 Recognize that translations,
reflections and rotations preserve
congruency and sue them to show that
two figures are congruent.
Grade 5 Standard
Grade 6 Standard 3.3: Choose
appropriate units of measurement
and use ratios to convert within
measurement systems to solve realworld and mathematical problems.
Benchmarks The student will:
There are no further standards in
this category for 5th grade.
6.3.3.1 Solve problems in various
contexts involving conversion of
weights, capacities, geometric
measurements and times within
measurement systems using
appropriate units.
6.3.3.2 Estimate weights, capacities
and geometric measurements using
benchmarks in measurement
systems with appropriate units.
Example: Estimate the height of a
house by comparing to a 6-foot man
standing nearby.
Example: A chocolate bar costs $1.84.
You pay for it with $2. Give two
possible ways to make change.
3.3.3.4 Use an analog thermometer to
determine temperature to the nearest
degree in Fahrenheit and Celsius.
Example: Read the temperature in a
room with a thermometer that has both
Fahrenheit and Celsius scales. Use the
thermometer to compare Celsius and
Fahrenheit readings.
MN Mathematics Standards - 2007 revision
Grades 3 - 6
13
IV.
Data Analysis
Grade 3 Standard 4.1: Collect,
Grade 4 Standard 4.1: Collect,
Grade 5 Standard 4.1: Display
Grade 6 Standard 4.1: Use
organize, display, and interpret data.
Use labels and a variety of scales and
units in displays.
organize, display and interpret data,
including data collected over a period
of time and data represented by
fractions and decimals.
and interpret data; determine mean,
median and range.
probabilities to solve real-world and
mathematical problems; represent
probabilities using fractions,
decimals and percents.
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
Benchmarks The student will:
3.4.1.1 Collect, display and interpret
data using frequency tables, bar graphs,
picture graphs and number line plots
having a variety of scales. Use
appropriate titles, labels and units.
4.4.1.1 Use tables, bar graphs,
timelines and Venn diagrams to
display data sets. The data may
include fractions or decimals.
Understand that spreadsheet tables
and graphs can be used to display
data.
5.4.1.1 Know and use the definitions
of the mean, median and range of a
set of data. Know how to use a
spreadsheet to find the mean,
median and range of a data set.
Understand that the mean is a
“leveling out” of data.
6.4.1.1 Determine the sample size
(set of possible outcomes) for a
given experiment and determine
which members of the sample space
are related to certain events.
Sample space may be determined
by the use of tree diagrams, tables
or pictorial representations.
Example: The set of numbers 1, 1, 4,
6 has mean 3. It can be leveled by
taking one unit from the 4 and three
units from the 6 and adding them to the
1s, making four 3s.
5.4.1.2 Create and analyze doublebar graphs and line graphs by
applying understanding of whole
numbers, fractions and decimals.
Know how to create spreadsheet
tables and graphs to display data.
Example: A 6  6 table with entries
such as (1,1), (1,2), (1,3), …, (6,6) can
be used to represent the sample space
for the experiment of simultaneously
rolling two number cubes.
6.4.1.2 Determine the probability of
an event using the ratio between the
size of the event and the size of the
sample space; represent
probabilities a percents, fractions
and decimals between 0 and 1
inclusive. Understand that
probabilities measure likelihood.
Example: Each outcome for a
balanced number cube has
probability 1 , and the probability of
6
rolling an even number is
MN Mathematics Standards - 2007 revision
Grades 3 - 6
1
2
.
14